**Add and subtract radical expressions :**

When we want to add or subtract two or more radical terms, first we have to verify whether they are having same number inside the radical sign or not.

The terms which are having same number inside the radical sign is known as like radicals.

Because we can add or subtract only like radical terms.

Some times we will have a large number inside the radical sign, that time we have to split the number inside the radical sign as much as possible and we can take one common number for every two same numbers multiplying inside the radical sign and make it as like radicals.

**Let us see some example problems to understand the concept. **

**Example 1 :**

Simplify the radical expression given below

√3 + √12

**Solution :**

= 3 √3

Hence 3 √3 is the answer.

**Example 2 :**

Simplify the radical expression given below

√75 + √25

**Solution :**

= √75 + √25

Here the given two radical terms are not like terms.

= √(5 x 5 x 5) + √(5 x 5)

= 5 √5 + 5

= 6 √5

**Example 3 :**

Simplify the radical expression given below

√7 + √49

**Solution :**

= √7 + √49

Since 7 is prime number, we cannot split this hereafter. We can split 49.

= √7 + √(7 x 7)

= √7 + 7

**Example 4 :**

Simplify the radical expression given below

√5 + 2√5 - 5√5

**Solution :**

= √5 + 2√5 - 5√5

Since √5 is common for all three terms, we are going to take √5 commonly from all the terms and simplify the numbers.

= (1 + 2 - 5) √5

= (3 - 5) √5

= -2 √5

**Example 5 :**

Simplify the radical expression given below

√5 + 3 √7 - 4 √5 - 5 √7

**Solution :**

= √5 + 3 √7 - 4 √5 - 5 √7

Now we have to group the like radicals.

= √5 - 4 √5 + 3 √7 - 5 √7

= (1 - 4) √5 + (3 - 5) √7

= - 3 √5 - 2 √7

**Example 6 :**

Simplify the radical expression given below

3√3 + 4 √3 - √2

**Solution :**

= 3√3 + 4 √3 - √2

The first two terms are having √3. Hence they are like radicals, we can combine them.

= (3 + 4) √3 - √2

= 7 √3 - √2

**Example 7 :**

Simplify the radical expression given below

2(√5 - √3) + 3(√3 - √5)

**Solution :**

= 2(√5 - √3) + 3(√3 - √5)

Distribute 2 for (√5 - √3) and distribute 3 for (√3 - √5).

= 2√5 - 2√3 + 3√3 - 3√5

Now we have to combine the like terms

= 2√5 - 3√5 - 2√3 + 3√3

= (2 - 3)√5 + (-2 + 3)√3

= -1√5 + 1√3

= -√5 + √3

**Example 8 :**

Simplify the radical expression given below

√8 + √18

**Solution :**

= √8 + √18

We can split 8 and 18 as much as possible to get factors.

= √(2 x 2 x 2) + √(2 x 3 x 3)

= 2√2 + 3√2

= (2 + 3) √2

= 5 √2

**Example 9 :**

Simplify the radical expression given below

√12w + √27w

**Solution :**

= √12w + √27w

We can split 12 and 27 as much as possible to get factors.

= √(2 x 2 x 3 x w) + √(3 x 3 x 3 x w)

= 2√(3 x w) + 3√(3 x w)

= 2√3w + 3√3w

= (2 + 3)√3w

= 5√3w

**Example 10 :**

Simplify the radical expression given below

√45t^2 + √25t^3

**Solution :**

= √45t^3 + √20t^3

We can split 45 and 25 as much as possible to get factors.

= √(3 x 3 x 5 x t^3) + √(2 x 2 x 5 x t^3)

= 3 t √5t + 2 t√5t

= (3 t + 2t) √5t

= 5t √5t

- Properties of radicals
- Simplifying radical expressions worksheets
- Square roots
- Ordering square roots from least to greatest
- Operations with radicals
- How to simplify radical expressions

After having gone through the stuff given above, we hope that the students would have understood "Add and subtract radical expressions".

Apart from the stuff given above, if you want to know more about "Add and subtract radical expressions", please click here

Apart from the stuff "Add and subtract radical expressions", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**